Concerning the norm of biquaternions and some other algebras with central conjunction
2004jbw | Eliovich A. A.

The concept of central conjunction is introduced in this article. We apply it to algebras of biquaternions and bioctaves. With the given analysis method of the conjunctions permitted by algebra we derive some new results. Thus the alternative algebras with central conjunction are proven to have the multiplicative norm of second degree (that is in general not real). The consequence of this fact is that these algebras (biquaternions and bioctaves particulary) have the multiplicative real norm of degree higher than 2. This norm has several different but equivalent views. The quadrascalar and quadravector multiplications are introduced. Some results for algebras of biquternions, diquaternions and bioctaves are given in terms of isotropic basis. The developed methods may be useful in the geometrical and physical usage of concerned algebras.

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